Turning to the Evidence: What Teachers Learn About Using Classroom Records and Artifacts in Mathematics Instruction

在这个项目中，研究人员建议检查教师如何在自己的专业发展中使用学生创造的数学学习人工制品。提案的概念框架来自两方面的工作。第一部分涉及教师用来理解学生思维的概念系统的理论和研究。最近，一些研究者将数学教育的认知图式描述为教育者感知、组织和实施其实践的“透镜”。研究人员认为，有两个镜头与教师识别和解释学生从课堂文物和记录中思考的证据的方式特别相关：一个“数学内容”镜头和一个“数学认识论”镜头。第二个概念链来自实践的情境性理论，它强调知识本身是其发展的环境的功能。尽管以实践为基础的专业发展旨在缩小教师在专业发展环境中的学习与课堂实践任务之间的距离，但两者之间的差异仍然是显著的。该项目将调查两个主要问题：(1)教师通过参与使用课堂记录和文物的专业发展学习到什么？(2)教师将他们学习的哪些方面应用到课堂实践中？该研究将调查教师的学习情况，因为他们参加了两个专业发展项目中的一个，这两个专业发展项目侧重于课堂文物分析，培养代数思维工具包（TK）或数学专业发展视频案例（VCM）。已经选定了四个地点，两个传统知识和两个VCM研讨会。与未参加治疗的教师的比较将包括在内。研讨会将每月举行一次，为期三个学期。与教师在研讨会中学习有关的数据将包括：教师对代数理解的前后测量，教师对学生作业样本的分析的前后访谈，研讨会的视频记录和现场笔记，以及教师对学生思维分析的嵌入式评估。关于课堂实践应用的数据将包括对研究中所有教师的课前/课后观察录像（观察包括课前和课后与教师的简报）以及对目标教师样本的月度观察。将与未参加专业发展计划的教师进行其中一些措施的比较。数据分析将酌情结合跨案例分析和定量比较。

In this project, the researchers propose to examine how teachers use student created artifacts of mathematics learning in their own professional development. The conceptual framing for the proposal comes from two strands of work. The first strand involves theory and research about the conceptual systems teachers use to understand student thinking. Several investigators have recently described cognitive schemata for mathematics education as "lenses" through which educators perceive, organize, and enact their practice. The researchers posit that two lenses are particularly relevant to the way teachers identify and interpret evidence of student thinking from classroom artifacts and records: a "mathematical content" lens and a "mathematical epistemology" one. The second conceptual strand comes from theories of the situated nature of practice, which emphasize that knowledge itself is a function of the contexts in which it develops. Although practice-based professional development seeks to narrow the distance between the learning teachers do in professional development settings and tasks of classroom practice, the differences between the two contexts can nonetheless be significant. The project will investigate two overarching questions: (1) what do teachers learn by participating in professional development that uses classroom records and artifacts? and (2) what aspects of their learning do teachers apply to their classroom practice? The study will investigate teachers' learning as they participate in either one of two professional development programs that focus on analysis of classroom artifacts, Fostering Algebraic Thinking Toolkit (TK) or VideoCases for Mathematics Professional Development (VCM). Four sites have been selected, two TK and two VCM seminars. Comparisons to teachers not in the treatment will be included. Seminars will meet monthly for three semesters. Data bearing on questions about teachers' learning in the seminars will include: pre/post measures of teachers' algebra understanding, pre/post interviews focusing on teachers' analysis of student work samples, video records and field notes of seminar sessions, and embedded assessments of teachers' analyses of student thinking. Data about the application to classroom practice will include videotaped pre/post classroom observations of all teachers in the study (observations include briefings with teachers before and after the lesson) and monthly observations of a sample of target teachers. A comparison on some of these measures will be made with teachers who do not participate in the professional development programs. Data analysis will involve a combination of cross-case analyses and quantitative comparisons, where appropriate.